In this paper we approach the question of the existence of a x, p phase space in a new way. Rather than abandoning all hope of constructing such a phase-space for quantum phenomena, we take aspects from both the Wigner-Moyal and Bohm approaches and show that although there is no unique phase space we can form ‘shadow’ phase spaces. We then argue that this is a consequence of the noncommutative ...

The purpose of this paper is to show that we can define different vector potentials in the problems of Aharonov-Bohm type, in such a way that they give the same physical results as the one originally proposed by Aharonov and Bohm, except in the regions of space where the fields become singular. We argue that a modified quantization condition comes out for the electric charge that may open up th...